How can i give my 3d ring a design with waves and other lines?
Topics:

UV mapping: how to map an image onto a mesh.
Shader Nodes: how to use images in various ways in your material, not just color.

In short, you need to UV map (nothing to do with ultraviolet) the ring’s outside. You can probably get the desired result by (with the proverbial finger of the ring pointing straight up):

selecting the top and bottom borders of the ring,
then selecting a slice of edges to break that into a strip when it unwraps,
marking all those edges as seams,
and then selecting all the outside of the ring (everything that falls inside that strip),
and “UV unwrap”-ing.

If that UV mapped the way I think it will, then using an image such as the one shown above in the ring’s material should wrap around it.